Temporal Databases: Queries

Temporal Databases: Queries
Kristian Torp
Department of Computer Science
Aalborg University
people.cs.aau.dk/˜torp
torp@cs.aau.dk
November 2, 2015
daisy.aau.dk
Kristian Torp (Aalborg University) Temporal Databases: Queries November 2, 2015 1 / 122

Outline
1 Overview and Foundation
Current, Valid Time, Transaction Time, and Bitemporal
Overlap Between Intervals
2 Temporal Join
3 Aggregation
4 Coalescing
5 Set Operators
6 Timeslice
Valid Time
Bitemporal
7 Summary

Learning Goals
Learning Goals
Understand the differences between valid time and transaction time
Understand bitemporal support
Temporal queries: aggregation, join, and timeslicing
Temporal interval and overlap
Note
The four-timestamp data model used is widely supported
n person will make at least n + 1 temporal data models
Words period and interval are central
And switched English versus SQL

Outline
2 Temporal Join
3 Aggregation
4 Coalescing
5 Set Operators
6 Timeslice
Valid Time
Bitemporal
7 Summary

Bitemporal Graphs: Explicit Valid Time
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill, Prozac
Bill, Prozac
Bill, Prozac
Bill, Morphine

Temporal Data: Tabular Overview
pname medicine
Bill Prozac
Bill Morphine
pname medicine vts vte tts tte
Bill Prozac 1 6 1 5
Bill Prozac 1 13 5 8
Bill Prozac 1 9 8 UC
Bill Morphine 10 15 2 UC
Current Bitemporal
pname medicine vts vte
Bill Prozac 1 9
Bill Morphine 10 15
pname medicine tts tte
Bill Prozac 1 5
Bill Prozac 5 8
Bill Prozac 8 UC
Bill Morphine 2 UC
Valid Time Transaction Time

Bitemporal Graphs: Implicit Valid Time
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, Shoe Joe, Shoe
Joe, Toy Joe, Toy
Joe, Shoe

Overview: Tabular Form
ename dept
Joe Shoe
ename dept vts vte tts tte
Joe Shoe 1 now 1 5
Joe Shoe 1 5 5 UC
Joe Toy 5 now 5 10
Joe Toy 5 10 10 UC
Joe Shoe 10 now 10 UC
Current Bitemporal
ename dept vts vte
Joe Shoe 1 5
Joe Toy 5 10
Joe Shoe 10 now
ename dept tts tte
Joe Shoe 1 5
Joe Toy 5 10
Joe Shoe 10 UC
Valid Time Transaction Time

now in Real Life
Examples of now in data
Marriage certificate
Hiring period
Permanent salary benefits
How long you have owned your car/house/dog
Office room allocation
Sickness period
Note
When end-date is uncertain/unknown/unspecified use now
Interpretation of now different valid time and transaction time
Also called until changed (UC) for transaction time

Valid Time or Transaction Time?
What do you think?
Reservation time this room this seminar?
The appointments in your calendar?
The timestamps in a GPS log from a vehicle?
The positions that you have held listed on your CV?
File modiﬁcation timestamp?
TV commercial: “Offer only valid next week!”
Web log?
Mortgage loan period?
Diary?
Bank day/date (tricky)?
Birthday (tricky)?

Outline
2 Temporal Join
3 Aggregation
4 Coalescing
5 Set Operators
6 Timeslice
Valid Time
Bitemporal
7 Summary

Allen’s Operators
0 1 2 3 4 5 6 7 8 9 10 11 12
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
X
Note
13 cases are complete
How intervals can overlap
The symmetries
Half-open/closed intervals
Does not matter!
All cases have names
Some of them are weird
J.F.Allen CACM 26(11), Nov.
1983

Simpliﬁed Overlap Operators
Example (Allen)
0 1 2 3 4 5 6 7 8 9 10 11 12
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
X
Example (Simpliﬁed)
0 1 2 3 4 5 6 7 8 9 10 11 12
Y Y
Y
Y
Y
Y
X

Names Simpliﬁed Overlap Operators
Example (Naming)
0 1 2 3 4 5 6 7 8 9 10 11 12
Before After
Left Overlaps
During
Right Overlaps
Total Overlaps
X
Note
These names are not ofﬁcial just used for reference in this
presentation.

Five Cases Simpliﬁed Overlap Operators
Example (The Cases)
0 1 2 3 4 5 6 7 8 9 10 11 12
Y Y
Y
Y
Y
Y
X
The Boolean Expressions
Case Expression
No Y.vte ≤ X.vts or X.vte ≤ Y.vts
Right X.vts < Y.vts and Y.vts < X.vte
Left X.vts < Y.vte and Y.vte < X.vte
Full Y.vts ≤ X.vts and X.vte ≤ X.vte
Do intervals overlap?
X.vts < Y.vte AND Y.vts < X.vte
Get Overlap
[greatest(X.vte, Y.vte), least(X.vts, Y.vts))
provided that the intervals X and Y overlap

Query Types: Current, Sequence, and Non-Sequenced
Note
Current state for backwards compatibility
Sequenced for built-in temporal semantic/support
Non-sequenced for accessing timestamps columns directly

Valid Time versus Transaction Time
Exercise
In groups, use 3 minutes to compare valid time and transaction time.

Exercise
Valid Time
Past, present, and future
User supplied
Supports now
Physical delete
“History correction”
Transaction Time
Past and present
System supplied
Supports now
Logical delete
History preserving (log)

Exercise
Valid Time
Past, present, and future
User supplied
Supports now
Physical delete
“History correction”
Transaction Time
Past and present
System supplied
Supports now
Logical delete
History preserving (log)
Valid Time for sure if:
Time is into the future
Time can be supplied by the user

Summary: Motivation I
Valid, Transaction, and User-Defined Time
Valid time and transaction time are orthogonal
Valid time: Past, present, and future
Can be user-defined (default similar to transaction time)
Transaction time: Past and present
Always system defined
User-defined time (if not valid time or transaction time)
e.g., birthday
Query Types
Current
Sequenced
Non-sequenced

Summary: Motivation II
Database Variables
Special variable now
Different semantics valid time and transaction time
Databases do not support variables
now = 9999-12-31 (maximum value of date domain)
Intervals
Timestamps are half-open intervals
Closed intervals +/- 1 therefore more complicated
Overlap between intervals is essential to understand
Not difﬁcult
5 cases to consider

Outline
2 Temporal Join
3 Aggregation
4 Coalescing
5 Set Operators
6 Timeslice
Valid Time
Bitemporal
7 Summary

The Idea: One
Example (Emp)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Joe, HR
Kim, HR
Example (Dept)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
HR, 10
Example (Emp Temporal Natural Join Dept)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Joe, HR, 10
Kim, HR, 10

The Idea: Two
Example (Emp)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Joe, HR
Kim, HR
Example (Dept)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
HR, 10
HR, 20
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Joe, HR, 10
Kim, HR, 10
Kim, HR, 20

The Idea: Three
Example (Emp)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Joe, HR
Kim, HR
Example (Dept)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
HR, 5
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

The Idea: Four
Example (Emp)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Joe, HR
Kim, RD
Example (Dept)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
HR, 10
RD, 20
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Joe, HR, 10
Kim, RD, 10

Natural Join Informal Deﬁnition
Idea Temporal Natural Join
The explicit attribute must be equal
The intersection of the timestamp intervals must be non-empty
The Overlap Cases to Consider
0 1 2 3 4 5 6 7 8 9 10 11 12
Before After
Left Overlaps
During
Right Overlaps
Total Overlaps
X

Temporal Natural-Join Example
select cname , adr , ptype , p . vts , p . vte −− t o t a l overlap
from c u s t v t as c , property vt as p
where c . cid = p . cid
and c . vts <= p . vts and p . vte <= c . vte union
select cname , adr , ptype , c . vts , p . vte −− r i g h t overlap
and c . vts between p . vts and p . vte
and c . vte > p . vte union
select cname , adr , ptype , p . vts , c . vte −− l e f t overlap
and c . vte between p . vts and p . vte
and c . vts < p . vts union −− during
select cname , adr , ptype , c . vts , c . vte
and c . vts between p . vts and p . vte
and c . vte between p . vts and p . vte

Quiz: What is the Natural-Join Result
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Bill, support
Pam, sale Pam, RD Pam, RD
Sam, RD
Jim, RD Jim, sale Jim, RD
Tim, web Tim, sale
Tom, sale Tom, test
Joe, RD Joe, sale Joe, RD
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
RD, 50 RD, 60 RD, 80
sale, 10 sale, 20 sale, 25
web, 5
test, 20 test, 15
support, 30

Summary: Temporal Join
Main Points
Temporal natural join most widely used
Like in non-temporal databases
Valid-time natural-join complicated because multiple overlap
scenarios to consider
It is possible to join a valid-time table with a non-temporal table
On all rows in the non-temporal table the valid-time is [-forever, forever)
Note
Efﬁciency may be a problem
Can you see why?
Temporal versions of Cartesian product, outer joins, and equi join are
well-deﬁned
See www.cs.arizona.edu/projects/stagg/papers/TR-71.pdf

Outline
2 Temporal Join
3 Aggregation
4 Coalescing
5 Set Operators
6 Timeslice
Valid Time
Bitemporal
7 Summary

The Data Foundation
Query in English
Find the number of persons employed over time and in which intervals.
Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Joe, 10 Joe, 12 Joe, 13
Jim, 12 Jim, 14
Jill, 10 Jill, 15
Pat, 9 Pat, 9 Pat, 10
Bill, 9
Boris, 9
Pam, 11
Kurt, 11

Constant Regions
Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Joe, 10 Joe, 12 Joe, 13
Jim, 12 Jim, 14
Jill, 10 Jill, 15
Bill, 9
Boris, 9
Pam, 11
Kurt, 11
Note
Vertical lines at all vts and vte values

The Result
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Joe, 10 Joe, 12 Joe, 13
Jim, 12 Jim, 14
Jill, 10 Jill, 15
Bill, 9
Boris, 9
Pam, 11
Kurt, 11 cnt vts vte
3 1 3
5 3 5
5 5 6
6 6 7
5 7 11
4 11 13
5 13 14
5 14 16
6 16 17
5 17 18
6 18 19
5 19 21
5 21 23
4 23 24

Main Idea in Finding Constant Regions
Five cases to consider
No other interval overlaps me
Another interval has vts between my vts and vte
Another interval has vte between my vts and vte
Another interval totally overlaps me
Another interval is after me
Note
For each case there can be no vts or vte between returned result
A single interval can qualify for more than one of the cases above
SQL is declarative therefore ”after” could be ”before”
But just one of the cases can be considered

Main Query
Example (The Main Query)
select count (ename) as cnt ,
const regions . vts as vts ,
const regions . vte as vte
from emp vt , const regions
where emp vt . vts < const regions . vte
and const regions . vts < emp vt . vte
group by const regions . vts , const regions . vte
order by vts , vte

Constant Regions Part 1: No Overlap
with const regions as (
−− get t1 . vts and t1 . vte
select t1 . vts as vts , t1 . vte as vte
from emp vt t1
where not exists (
select ∗
from emp vt t3
where ( t1 . vts < t3 . vts and t3 . vts < t1 . vte ) or
( t1 . vts < t3 . vte and t3 . vte < t1 . vte ) )
Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
result = t1
not exists t3
not exists t3

Constant Regions Part 2:
union
−− t1 . vts and t2 . vts
select t1 . vts as vts , t2 . vts as vte
from emp vt t1 , emp vt t2
where t1 . vts < t2 . vts and t2 . vts < t1 . vte
and not exists (
select ∗
from emp vt t3
where ( t1 . vts < t3 . vts and t3 . vts < t2 . vts ) or
( t1 . vts < t3 . vte and t3 . vte < t2 . vts ) )
Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
t1
t2
result

union
−− t1 . vts and t2 . vte
select t1 . vts as vts , t2 . vte as vte
where t1 . vts < t2 . vte and t2 . vte < t1 . vte
and not exists (
select ∗
from emp vt t3
where ( t1 . vts < t3 . vts and t3 . vts < t2 . vte ) or
( t1 . vts < t3 . vte and t3 . vte < t2 . vte ) )
Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
t1
t2
result

Constant Regions Part 4: Before
union
−− t1 . vte and t2 . vts
select t1 . vte as vts , t2 . vts as vte
where t1 . vte < t2 . vts
and not exists (
select ∗
from emp vt t3
where ( t1 . vte < t3 . vts and t3 . vts < t2 . vts ) or
( t1 . vte < t3 . vte and t3 . vte < t2 . vts ) )
Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
t1
t2
result

union
−− t1 . vte and t2 . vte
select t1 . vte as vts , t2 . vte as vte
where t2 . vts < t1 . vte and t1 . vte < t2 . vte
and not exists (
select ∗
from emp vt t3
where ( t1 . vte < t3 . vts and t3 . vts < t2 . vte ) or
( t1 . vte < t3 . vte and t3 . vte < t2 . vte ) ) )
Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
t1
t2
result

Correctness of Constant Regions
Five = Original row + Four Combinations
[t1.vts, t1.vte)
[t1.vts, t2.vts)
[t1.vts, t2.vte)
[t2.vte, t2.vts)
[t2.vte, t2.vte)
Note
All cases are covered
Informal argument

Quiz
Query in English
Find the constant regions and average budget for all departments over
time.
Example (Data Foundation)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
RD, 50 RD, 60 RD, 80
web, 5
test, 20 test, 15
support, 30

Quiz: Solution, One
Example (Data Foundation with Dividers)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
RD, 50 RD, 60 RD, 80
web, 5
test, 20 test, 15
support, 30
Rest of Solution
Now we have the constant regions
Next step is to do the aggregation within each region

Quiz: Solution, Two
cnt vts vte
50.00 1 4
30.00 4 6
21.67 6 8
21.25 8 10
26.67 10 11
33.33 11 15
33.75 15 16
32.50 16 17
37.50 17 22
45.00 22 24
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
50.00
30.00
21.67
21.25
26.67
33.33
33.75
32.50
37.50
45.00

Summary: Aggregation
Main Points
Constant regions must be identified
Can be done in multiple ways
Approach used is consider efficient (allowed to prove me wrong :-))
Due to various ways intervals may overlap the queries are long
Same approach to average, count, minimum, and so on
Note
The approach also works if grouping on non-temporal column
It is an exercise to figure-out how!

Outline
2 Temporal Join
3 Aggregation
4 Coalescing
5 Set Operators
6 Timeslice
Valid Time
Bitemporal
7 Summary

Coalescing in Figures
Example (How long have Lars and Peter been with us?)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Lars, web Lars, web
Lars, web
Lars, test Lars, test
Peter, web Peter, test Peter, test

Coalescing in Figures
Example (How long have Lars and Peter been with us?)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Lars, web Lars, web
Lars, web
Example (Result)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Lars
Peter
Note
Select just the employee name
Coalescing resulted in fewer rows

Coalescing in Figures, cont
Example (How long have the ’web’ and ’test’ projects been active?)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Lars, web Lars, web
Lars, web

Coalescing in Figures, cont
Example (How long have the ’web’ and ’test’ projects been active?)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Lars, web Lars, web
Lars, web
Example (Result)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
test
web web
Note
Coalescing gives better overview
Coalescing gives new insight

Example: Valid-Time State Data Model
Example (State and Event)
pname vts vte
Bush 1989 1993
Clinton 1993 1997
Clinton 1997 2001
Bush jr. 2001 2005
Bush jr. 2005 2009
Obama 2009 2013
Obama 2013 2017
pname vts vte
Bush 1989 1993
Clinton 1993 2001
Bush jr. 2001 2009
Obama 2009 2017
Questions
Do the tables have the same content?
Does it have anything to do with duplicate elimination?
What can you say about primary keys (tricky)?

Example: Event Data Model
Example (Similar Content)
pname vts vte
Bush 1989 1993
Clinton 1993 1997
Clinton 1997 2001
Bush jr. 2001 2005
Bush jr. 2005 2009
Obama 2009 2013
Obama 2013 2017
pname vts
Bush 1989
Clinton 1993
Clinton 1997
Bush jr. 2001
Bush jr. 2005
Obama 2009
Obama 2013
pname vts
Bush 1989
Clinton 1993
Bush jr. 2001
Obama 2009
Questions
Any implicit assumptions for state or event table?
Future data any differences?
What are the pros/cons state versus event table?

Quiz: Coalescing
Questions
How much space can be saved coalescing temporal data?
Informal argument using examples!
Can data in valid-time event tables be un-coalesced?

Quiz: Coalescing
Questions
How much space can be saved coalescing temporal data?
Can data in valid-time event tables be un-coalesced?
Answers
The saving coalescing the data stored can be signiﬁcant. Consider
many overlaps of value equivalent rows.
Event-tables can also be un-coalesced.

Advantages and Disadvantages
Coalesced
Minimal space
Row delete info. lost
Queries faster
Less data
Modiﬁcations slower
Many checks
Un-coalesced
Additional space
Possibly much larger
Queries slower
More data
Modiﬁcations faster
Less checking

Coalescing in SQL (Proposed by Celko/Bohlen)
select d i s t i n c t f i . ename, f i . vts , la . vte
from projemp vt f i , projemp vt la
where f i . vts < la . vte
and f i . ename = la . ename
and not exists ( −− ensure no holes and extend towards f i . vts
select ∗
from projemp vt mi
where mi . ename = f i . ename
and f i . vts < mi . vts and mi . vts < la . vte
and not exists (
select ∗
from projemp vt a1
where a1 . ename = f i . ename
and a1 . vts < mi . vts and mi . vts <= a1 . vte ) )
and not exists ( −− ensure only maximal periods
select ∗
from projemp vt a2
where a2 . ename = f i . ename
and ( a2 . vts < f i . vts and f i . vts <= a2 . vte
or a2 . vts <= la . vte and la . vte < a2 . vte ) )
order by f i . ename, f i . vts

Quiz: Coalesced?
Example (Is the data coalesced?)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Joe, Shoe Joe, Shoe Joe, Toy
Tom, Shoe Tom, Shoe Tom, Toy

Quiz: Coalesced?
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Tom, Shoe Tom, Shoe Tom, Toy
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Tom, Shoe
Tom, Toy

Questions Related to Coalesced
Questions
Can coalescing increase the number of rows in table?
What happens if you coalesce a table/query twice?
If you make a projection on a coalesce table is the result coalesced?
If you make a selection on a coalesce table is the result coalesced?
Are ename and vts a primary key of a coalesced table?

Summary: Coalescing
Main Points
Similar to duplicate elimination
also called fold/unfold
Coalesced = uncoalesed is domain speciﬁc
Follow the data
Can data be coalesced without information loss?
Note
Avoid making coalescing into “politics” or “religion”
Some persons have strong feelings for/against coalescing
Coalescing is an expensive operation to perform
It is related to duplicate elimination
Nothing to do with the coalesce function
Do you know what this function does?
Additional information on coalescing
timecenter.cs.aau.dk/TimeCenterPublications/TR-9.pdf

Outline
2 Temporal Join
3 Aggregation
4 Coalescing
5 Set Operators
6 Timeslice
Valid Time
Bitemporal
7 Summary

Overview
Example (One)
VT
0 1 2 3 4 5 6 7 8 9 10
R
S
R ∪ S
R ∩ S
VT
0 1 2 3 4 5 6 7 8 9 10
R
S
R − S
S − R

Overview
Example (One)
VT
0 1 2 3 4 5 6 7 8 9 10
R
S
R ∪ S
R ∩ S
VT
0 1 2 3 4 5 6 7 8 9 10
R
S
R − S
S − R
Example (Two)
VT
0 1 2 3 4 5 6 7 8 9 10
R
S
R ∪ S
R ∩ S
VT
0 1 2 3 4 5 6 7 8 9 10
S
R − S
S − R

Overview
Example (One)
VT
0 1 2 3 4 5 6 7 8 9 10
R
S
R ∪ S
R ∩ S
VT
0 1 2 3 4 5 6 7 8 9 10
R
S
R − S
S − R
Example (Two)
VT
0 1 2 3 4 5 6 7 8 9 10
R
S
R ∪ S
R ∩ S
VT
0 1 2 3 4 5 6 7 8 9 10
S
R − S
S − R
Note
Think Venn diagrams
No big surprises!

Set Intersection: As Figure
Example (Emp1)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Jens Jens
Lene Lene
Example (Emp2)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Jens
Lene Lene

Set Intersection: As Figure
Example (Emp1)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Jens Jens
Lene Lene
Example (Emp2)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Jens
Lene Lene
Example (Emp1 ∩ Emp2)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Jens
Lene Lene

Set Intersection: As Table
Example (Emp)
ename dept vts vte
Jens RD 0 5
Lene Cust 2 10
Jens Sup 6 15
Jens Cust 16 20
Example (Boss)
ename dept vts vte
Lene Cust 5 9
Jens Cust 17 20
Example (Emp ∩ Boss)
ename dept vts vte
Lene Cust 5 9
Jens Cust 17 20

Set Intersection: The Cases
Example (Before)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
empty
Example (After)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
empty
Example (Right Overlap)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result
Example (Left Overlap)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result
Example (Included)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result
Example (Totally Overlaps)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result

Set Intersection: Informally
Deﬁnition
Explicit columns must be equal
If overlap between the intervals then take the
The largest of the vts values
The smallest of the vte values
Otherwise skip the row
Note
Recall that vts ≤ vte for interval to be valid

Set Intersection in SQL
select emp. ename, emp. dept , −− overlap emp and boss
greatest (emp. vts , boss . vts ) as vts ,
least (emp. vte , boss . vte ) as vte
from emp dept vt as emp, bossemp dept vt as boss
where emp. ename = boss . ename and emp. dept = boss . dept
and emp. vts < boss . vte and boss . vts < emp. vte
and greatest (emp. vts , boss . vts ) <= least (emp. vte , boss . vte )

Set Union: As Figure
Example (Emp1)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Jens Jens
Lene Lene
Example (Emp2)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Jens
Lene Lene

Set Union: As Figure
Example (Emp1)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Jens Jens
Lene Lene
Example (Emp2)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Jens
Lene Lene
Example (Emp1 ∪ Emp2)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Jens Jens
Lene Lene

Set Union: As Table
Example (Emp)
ename dept vts vte
Jens RD 0 5
Lene Cust 2 10
Jens Sup 6 15
Jens Cust 16 20
Example (Boss)
ename dept vts vte
Lene Cust 5 9
Jens Cust 17 20
Example (Emp ∪ Boss)
ename dept vts vte
Jens RD 0 5
Lene Cust 2 10
Jens Sup 6 15
Jens Cust 16 20

Set Union: The Cases
Example (Before)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result result
Example (After)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result result
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result
Example (Included)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result

Set Union: Informally
Deﬁnition
If overlap between the intervals then take the
The smallest of the vts values
The largest of the vte values
Else take the intervals in the ﬁrst table,
and take the intervals in the second table
Note
Three cases to consider
Mutual exclusive cases therefore union all between cases
The rows must be snapshot equal, i.e., have the same explicit
columns

Set Union in SQL
select emp. ename, emp. dept , −− overlap emp and boss
least (emp. vts , boss . vts ) as vts ,
greatest (emp. vte , boss . vte ) as vte
and emp. vts < boss . vte and boss . vts < emp. vte union a l l
select emp. ename, emp. dept , emp. vts , emp. vte −− emp no overlap
from emp dept vt as emp
where not exists (
select ∗
from bossemp dept vt as b
where emp. ename = b . ename and emp. dept = b . dept
and emp. vts < b . vte and b . vts < emp. vte ) union a l l
select boss . ename, boss . dept , boss . vts , boss . vte −− boss no overlap
from bossemp dept vt as boss
where not exists (
select ∗
from emp dept vt as b
where boss . ename = b . ename and boss . dept = b . dept
and boss . vts < b . vte and b . vts < boss . vte )
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−Kristian Torp (Aalborg University) Temporal Databases: Queries November 2, 2015 68 / 122

Set Difference: As Figure
Example (Emp)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Jens, RD Jens, Sup Jens, Cust
Lene, Cust
Example (Boss)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Jens, Cust
Lene, Cust
Example (Emp - Boss)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Jens, RD Jens, Sup Jens, Cust
Lene, Cust Lene, Cust

Set Difference: As Table
Example (Emp)
ename dept vts vte
Jens RD 0 5
Lene Cust 2 10
Jens Sup 6 15
Jens Cust 16 20
Example (Boss)
ename dept vts vte
Lene Cust 5 9
Jens Cust 17 20
Example (Emp - Boss)
ename dept vts vte
Jens RD 0 5
Lene Cust 2 5
Lene Cust 9 10
Jens Sup 6 15
Jens Cust 16 17

Set Difference: The Cases
Example (Before)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result
Example (After)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result
Example (Included)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
result result
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
emp
boss
empty

Set Difference: Informally
Deﬁnition
If overlap between the intervals then
Row with interval [emp.vts, boss.vts) if emp.vts< boss.vts
Row with interval [boss.vte, emp.vte) if boss.vte< emp.vte
Otherwise skip the row
Note
Before or after does not matter
Total overlap does not add rows to the result
During is handled like a combination of left and right overlap
One interval may be split into one or two intervals

Set Difference in SQL, Part 1
select emp. ename, emp. dept , emp. vts , emp. vte −− no overlap
from emp dept vt as emp
where not exists (
select ∗
and emp. vts < b . vte and b . vts < emp. vte )
union

Set Difference in SQL, Part 2
select emp. ename, emp. dept , emp. vts , boss . vts −− r i g h t overlap
and emp. vts < boss . vts and boss . vts < emp. vte and
not exists (
select ∗
and emp. vts < b . vte and b . vts < boss . vts )
union
select emp. ename, emp. dept , boss . vte , emp. vte −− l e f t overlap
and boss . vte < emp. vte and emp. vts < boss . vte and
not exists (
select ∗
and boss . vte < b . vte and b . vts < emp. vte )

Quiz: Set Operations
Questions
R ∪ S = S ∪ R ?

Questions
R ∪ S = S ∪ R ? Yes!
R ∩ S = S ∩ R ?

Questions
R ∪ S = S ∪ R ? Yes!
R ∩ S = S ∩ R ? Yes!
R − S = S − R ?

Questions
R ∪ S = S ∪ R ? Yes!
R ∩ S = S ∩ R ? Yes!
R − S = S − R ? No!
Can R ∪ S return fewer rows than there are in R?

Questions
R ∪ S = S ∪ R ? Yes!
R ∩ S = S ∩ R ? Yes!
R − S = S − R ? No!
Can R ∪ S return fewer rows than there are in R? Yes!
In contrast to the non-temporal version
Can R − S return more rows than there are in R?

Questions
R ∪ S = S ∪ R ? Yes!
R ∩ S = S ∩ R ? Yes!
R − S = S − R ? No!
Can R − S return more rows than there are in R? Yes!
In contrast with non-temporal version
Can R ∩ S return more rows than there are in R?

Questions
R ∪ S = S ∪ R ? Yes!
R ∩ S = S ∩ R ? Yes!
R − S = S − R ? No!
Can R ∩ S return more rows than there are in R? Yes!
Can R − S return an empty result?

Questions
R ∪ S = S ∪ R ? Yes!
R ∩ S = S ∩ R ? Yes!
R − S = S − R ? No!
Can R − S return an empty result? Yes!
Like the non-temporal version!
Can R ∩ S return an empty result?

Questions
R ∪ S = S ∪ R ? Yes!
R ∩ S = S ∩ R ? Yes!
R − S = S − R ? No!
Can R − S return an empty result? Yes!
Can R ∩ S return an empty result? Yes!

Summary: Set Operators
Main Points
No big surprises in how union, intersection, and difference are deﬁned
The size of the result sets may be a surprise!
Set difference is surprisingly difﬁcult
Challenge that single row can be split into two rows
Note
Notation of union compatibility still applies!
Alternative interpretations of the set operators exists
However not in widespread usage

Outline
2 Temporal Join
3 Aggregation
4 Coalescing
5 Set Operators
6 Timeslice
Valid Time
Bitemporal
7 Summary

Timeslicing: As a Figure
Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Joe, Shoe Joe, Toy
Jim, Toy
Jill, Shoe
Example (In Table Format)
ename dept vts vte
Joe Shoe 2 8
Joe Toy 10 now
Jim Toy 4 14
Jill Shoe 12 now

Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Joe, Shoe Joe, Toy
Jim, Toy
Jill, Shoe
Example (Timeslice at time 1)
ename dept

Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Joe, Shoe Joe, Toy
Jim, Toy
Jill, Shoe
ename dept
Joe Shoe

Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Joe, Shoe Joe, Toy
Jim, Toy
Jill, Shoe
ename dept
Jim Toy

Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Joe, Shoe Joe, Toy
Jim, Toy
Jill, Shoe
ename dept
Joe Toy
Jim Toy
Jill Shoe

Example
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Joe, Shoe Joe, Toy
Jim, Toy
Jill, Shoe
ename dept
Joe Toy
Jill Shoe
Note
Timeslicing can be both in valid time and transaction time

Outline
2 Temporal Join
3 Aggregation
4 Coalescing
5 Set Operators
6 Timeslice
Valid Time
Bitemporal
7 Summary

Current TimeSlice (now = 20)
Example (Content)
ename dept vts vte
Joe Shoe 2 8
Joe Toy 10 now
Jim Toy 4 14
Jill Shoe 12 now
Example (Timeslice)
ename dept
Joe Toy
Jill Shoe
Example (SQL Statement)
select ename, dept
from emp
where vte = 99 −− 99 i s the value used f o r now
Note
Only explicit attributes
SQL statement is simple

Timeslice Back in Time 13 (now = 20)
Example (Content)
ename dept vts vte
Joe Shoe 2 8
Joe Toy 10 now
Jim Toy 4 14
Jill Shoe 12 now
Example (Timeslice)
ename dept
Joe Toy
Jim Toy
Jill Shoe
Example (SQL Statement)
select ename, dept
from emp
where vts < 13 and vte >= 13
Note
between cannot be used due to half-open intervals
Query different from current timeslice
SQL statement again simple

Summmary: Valid-Time Timeslice
Main Points
Current state most often used
Timeslice back and forward in time same query
SQL statements are simple
Must pick a value for now
Typically 9999-12-30 or 9999-12-31
Transaction-time slicing basically the same as for valid-time
Note
Often current state separated from other data

Outline
2 Temporal Join
3 Aggregation
4 Coalescing
5 Set Operators
6 Timeslice
Valid Time
Bitemporal
7 Summary

First Example of Transaction-Time Timeslice
Example (Bitemporal Graph)
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, Shoe Joe, Shoe
Joe, Toy Joe, Toy
Joe, Shoe
Table Content
Content as of time 15
Only one employee, to make graph readable

Timeslice at 1
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, Shoe
ename dept vts vte
Joe Shoe 1 now

Timeslice at 2
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, Shoe
ename dept vts vte
Joe Shoe 1 now

Timeslice at 3
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, Shoe
ename dept vts vte
Joe Shoe 1 now

Timeslice at 4
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, Shoe
ename dept vts vte
Joe Shoe 1 now

Timeslice at 5
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, ShoeJoe, Shoe
Joe, Toy
ename dept vts vte
Joe Shoe 1 5
Joe Toy 5 now

Timeslice at 6
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, ShoeJoe, Shoe
Joe, Toy
ename dept vts vte
Joe Shoe 1 5
Joe Toy 5 now

Timeslice at 7
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, ShoeJoe, Shoe
Joe, Toy
ename dept vts vte
Joe Shoe 1 5
Joe Toy 5 now

Timeslice at 8
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, ShoeJoe, Shoe
Joe, Toy
ename dept vts vte
Joe Shoe 1 5
Joe Toy 5 now

Timeslice at 9
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, ShoeJoe, Shoe
Joe, Toy
ename dept vts vte
Joe Shoe 1 5
Joe Toy 5 now

Timeslice at 10
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, ShoeJoe, Shoe
Joe, ToyJoe, Toy
Joe, Shoe ename dept vts vte
Joe Shoe 1 5
Joe Toy 5 10
Joe Shoe 10 now

Timeslice at 11
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, ShoeJoe, Shoe
Joe, ToyJoe, Toy
Joe Shoe 1 5
Joe Toy 5 10
Joe Shoe 10 now

Timeslice at 12
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, ShoeJoe, Shoe
Joe, ToyJoe, Toy
Joe Shoe 1 5
Joe Toy 5 10
Joe Shoe 10 now

Timeslice at 13
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, Shoe Joe, Shoe
Joe, ToyJoe, Toy
Joe, Shoe
ename dept vts vte
Joe Shoe 1 5
Joe Toy 5 10
Joe Shoe 10 now

Timeslice at 14
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, Shoe Joe, Shoe
Joe, ToyJoe, Toy
Joe, Shoe
ename dept vts vte
Joe Shoe 1 5
Joe Toy 5 10
Joe Shoe 10 now

Timeslice at 15
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joe, Shoe Joe, Shoe
Joe, Toy Joe, Toy
Joe, Shoe
ename dept vts vte
Joe Shoe 1 5
Joe Toy 5 10
Joe Shoe 10 now

Summary: First Example
Note that
All previous states retained
Backward compatible (with “plain” SQL)
End-used has supplied no valid-time values
Transaction-time slice contains valid-time columns

Second Example of Transaction-Time Timeslice
Example (Bitemporal Graph)
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill, Prozac, Pepper
Bill, Morphine, Jones
Table Content
Content as of time 15
Only one patient

Timeslice at 1
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
pname medicin vts vte
Bill Prozac 1 6

Timeslice at 2
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill Prozac 1 6
Bill Morphine 10 15

Timeslice at 3
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill Prozac 1 6
Bill Morphine 10 15

Timeslice at 4
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill Prozac 1 6
Bill Morphine 10 15

Timeslice at 5
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill Prozac 1 13
Bill Morphine 10 15

Timeslice at 6
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill Prozac 1 13
Bill Morphine 10 15

Timeslice at 7
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill Prozac 1 13
Bill Morphine 10 15

Timeslice at 8
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill Prozac 1 9
Bill Morphine 10 15

Timeslice at 9
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill Prozac 1 9
Bill Morphine 10 15

Timeslice at 10
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill Prozac 1 9
Bill Morphine 10 15

Timeslice at 11
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill Prozac 1 9
Bill Morphine 10 15

Timeslice at 12
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill Prozac 1 9
Bill Morphine 10 15

Timeslice at 13
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill Prozac 1 9
Bill Morphine 10 15

Timeslice at 14
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill Prozac 1 9
Bill Morphine 10 15

Timeslice at 15
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Bill Prozac 1 9
Bill Morphine 10 15

Summary: Second Example
Note that
All previous states retained
Valid-time does not retain your errors!
However, bitemporal does!
Not-backwards compatible (with “plain” SQL)
End-used has supplied all valid-time values

Quiz: Does Bill Die?
Example (Medication for Bill)
TT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
VT
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Alive or Dead?
If prozac and morphine is a leathal combination does Bill die?

Summary: Timeslicing
Main Points
Timeslicing see the table as of a point in time
Timeslicing can be both in valid-time and transaction-time
For transaction-time timeslicing only into the past
For valid-time timeslicing both into the past and the future
Timeslicing is a fairly simple SQL select statement
Note
Current timeslice = the database state stored by non-temporal
databases
Physical database design: current timeslice stored separately from
other data

Outline
2 Temporal Join
3 Aggregation
4 Coalescing
5 Set Operators
6 Timeslice
Valid Time
Bitemporal
7 Summary

Quiz
Example (Emp Table One)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Joe, Shoe Joe, Toy Joe, Shoe
Tom, Shoe
Tom, Toy
Questions
Were Joe and Tom employed during the same period?
Did Joe and Tom work in the same department at the same time?
Is the data coalesced?

Quiz
Example (Emp Table Two)
VT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Joe, Shoe Joe, Toy Joe, Food
Tom, Food
Tom, Shoe
Tom, Toy
Tom, Toy
Questions
Were Joe and Tom employed during the same period?
Did Joe and Tom work in the same department at the same time?
Is the data coalesced?

Summary: Main Ideas
Query Types
Time dimensions: valid time, transaction time, and user-deﬁned time
Bitemporal = valid time + transaction time
Query types: current, sequenced, non-sequenced
Extensions of plain SQL: Join, aggregation, set operations
Also projection and selection
New possibilities: Timeslicing
New problems: Coalescing
Intervals overlap, central to understand how works
Not difﬁcult, just many cases
Note
A temporal data model implemented using plain SQL
IBM DB2 10, SQL Server 2015, and TeraData 13.10 have built-in
bitemporal support

Temporal Databases: Queries

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